Question

8. If the polynomials ax³ + 3x² - 13 and 5x³ - 8x + a leave the same remainder when
divided by x + 1, then find the value of a.​

Answer 1

Step-by-step explanation:

here's your answer

USING REMAINDER THEOREM...

$a {x}^{3} + 3 {x}^{2} - 13 = 5 {x}^{3} - 8x + a \\ \\ p(x) = - 1 \\ \\ a( - 1)^{3} + 3( { - 1}^{2} ) - 13 = \\ 5 ({ - 1}^{3} ) - 8( - 1) + a \\ \\ - a + 3 - 13 = - 5 + 8 + a \\ \\ - a - a = 3 - 3 + 13 \\ \\ - 2a = 13 \\ \\ a = \frac{ - 13}{2}$

Answer 2

Answer:

Step-by-step explanation:

Using remainder theorem

X+1 = 0

X= -1

ax³ + 3x² - 13 = p(x)

P( -1 ) = a(-1)³ + 3(-1)² - 13

-a - 10 = remainder

In 5x³ - 8x + a

Putting value of X as -1

5(-1)³ - 8(-1) + a

-5 +8 + a = 3+ a = remainder

Equalating remainders

3 + a = -a - 10

2a = -13

a = -13/2